Time-to-event crash severity prediction at highway-rail grade crossings with monotonic neural networks

Despite advances in highway-rail grade crossing (HRGC) safety, including widespread use of active control devices, crashes at these intersections still lead to severe outcomes. Conventional crash prediction models often fail to capture severity-level dependencies, rely on assumption-driven and computationally intensive methods, and overlook links between severity and time between events. This study introduces a predictive framework based on positive monotonic neural networks (MNNs) for modeling time-to-crash outcomes with severity at HRGCs. Considering the relative newness of the time-to-crash paradigm in HRGC safety, the Neural Fine-Gray model is adopted as a core MNN implementation to estimate severity-specific crash likelihoods. This approach eliminates the numerical integration required in traditional time-to-event models, substantially reducing computational burden and accelerating training for large datasets. The framework naturally handles imbalanced HRGC data by treating event-free records as right-censored, avoiding the resampling required in traditional machine-learning approaches. To examine severity-level dependencies-an aspect largely overlooked in the literature-four MNN architectures are developed and evaluated. Using a 29-year North Dakota HRGC dataset, results show trade-offs between predictive accuracy and computational efficiency. The cause-specific MNN performs best for medium- and long-term horizons, whereas the multi-head MNN converges faster and excels at short horizons. Moreover, benchmarking against traditional time-to-event models-cause-specific Cox and Fine-Gray-shows modest calibration gains and 2%-50% stronger discrimination, reflecting the alignment between MNNs and the nonlinear, high-dimensional HRGC data. The framework also enhances interpretability by revealing paradoxical effects, including the "adding flashing lights paradox" and the "adding stop signs paradox."